# Percentage Decrease Calculator

Decreased from
To
Percent Decrease  =  20%
GENERATE WORK

## Percentage Decrease - work with steps

Input Data :
From Value = 100
To Value = 80

Objective :
Find what percent decrease is from 100 to 80?

Formula

\text{Percent decrease} = \frac{\text{From Value - To Value}}{\text{From Value}} \times 100

Solution :
Percent decrease = \frac{100 - 80}{100} \times 100

 = \frac{20}{100} \times 100

 = \frac{2000}{100}

Percent decrease = 20%

Percentage decrease calculator uses two values, original $X$ and final $Y$ such that $X>Y$ and $X\ne 0$, and calculate the percent of decrease from the original to final. In other words, it determines the change of a quantity to a smaller amount in terms of percent. It is an online mathematical tool requires two real numbers, and finds the amount of a loss as a percentage of the original value.
It is necessary to follow the next steps:

1. Enter the original and final values in the box. The original value must be greater than the final. These values must be real numbers, whereas the original value must be nonzero;
2. Press the "GENERATE WORK" button to make the computation;
3. Percentage decrease calculator will give the percent of decrease from the first amount to the second one.
Input: Two real numbers, whereas the first one must be nonzero. Note that the first entered number must be greater than the second one.
Output: The result is a percent value, i.e. a positive real number and $\%$ after the number.

Percent of Decrease Formula:
If the original amount is greater than the final amount, then the percent of decrease is determined by the following formula
$$\rm{percent\;of\;decrease}=\Big(\frac{\rm{original\;amount-final\;amount}}{|\rm{original\;amount}|}\Big)\times 100\%, \quad\rm{original\;amount}\ne0$$

## What is Percent of Decrease?

A percent of change is increased or decreased the percent an amount in relation to the original amount. The formula for the percent change is

$$\rm{percent\;change}=\Big(\frac{\rm{final\;amount-original\;amount}}{|\rm{original\;amount}|}\Big)\times 100\%, \quad\rm{original\;amount}\ne0$$

or
$$\frac{\rm{percent\;change}}{100}=\Big(\frac{\rm{actual\;change}}{|\rm{original\;amount}|}\Big)\times 100\%, \quad\rm{original\;amount}\ne0$$
When an amount increases, i.e the percent change is positive, then the percent of change is a percent of increase. When an amount decreases, i.e the percent change is negative, then the percent of change is a percent of decrease.
For example, a rectangle has side lengths of $a=5$ and $b=3$ units. Suppose that the length of the side $a$ is decreased from $5$ to $2$ units. The original area of the rectangle is $15$ square units, but the the final area of the rectangle is $6$ square units. So, the area is decreased to $6$ square units. This is a change in area of $9$ square units. The relation between the original and new area can be expressed in terms of ratio:
\begin{align}\frac{\rm{percent\;change}}{100}&=\Big(\frac{\rm{changing\;in\;area}}{\rm{original\;area}}\Big)\times 100\%\\ &=\Big(\frac{\rm{final\;area-original\;area}}{\rm{original\;area}}\Big)\times 100\%\\ &=\Big(\frac{6-15}{15}\Big)\times 100\%\\ &=\frac{-9}{15}\times 100\%\\ &=-60\%\end{align}
The percent of change is $-60\%$. Since the percent of change is negative, the percent of change is a percent of decrease, so compared to the original area, the new area decreased by $60\%$.
For this reason, the percent of decrease is fully determined by the formula
$$\rm{percent\;of\;decrease}=\Big(\frac{\rm{original\;amount-final\;amount}}{|\rm{original\;amount}|}\Big)\times 100\%, \quad\rm{original\;amount}\ne0$$

If the percent of decrease and the original amount are known, we can find the final amount using the following formula:
$$\rm{final\;amount}=\rm{original\;amount}-{\rm{percent\;of\;decrease}\times|\rm{original\;amount}|}$$

### How to calculate Percent of Decrease

If the original amount is greater than the final amount, then the percent of change decreased. If the percent of change decreased, then the percent of change is a percent of decrease and vise versa. The percent of decrease is the difference between an original and final amounts divided by the absolute value of the original amount and multiplied by $100\%$.
The percentage decrease work with steps shows the complete step-by-step calculation for finding the percent of decrease from one amount to another with the original (initial) value of $100$ and the final value of $80$. For any other combinations of the original and final values, just supply values and click on the "GENERATE WORK" button. The grade school students may use this percent decrease calculator to generate the work, calculate the percent of change for some discount, verify the results or do their homework problems efficiently.

### Real World Problems Using Percent of Decrease

Since the percent of decrease describes an amount that has be reduced, an application of percent of decrease is in shopping with discounts. Some companies describe their failure as decrease in profit levels using the percent of decrease.

### Percentage Decrease Practice Problems

Practice Problem 1:
In $2010$, the population of Europe was $754,036,789.$ In $2018$, the population was $653,432,140.$ Find the percent of decrease from $2010$ to $2018$.

Practice Problem 2:
Find the percent of decrease from $510$ to $140$.

The Percentage Decrease Calculator, formula, example calculation (work with steps) and practice problems would be very useful for grade school students of K-12 education to learn how to find percent of decrease from one number to another. This concept is very useful in real-life, for instance, to find the discount and sale price of an item.